Chapter 1 Directed Number (2)

NAME: ………………………………………………………………… CLASS: 2TB2 DATE: …………………..

1

CHAPTER 1 DIRECTED NUMBER

Addition and Subtraction of Integers

1. –3 – 15 =

2. –4 + 17 =

3. –4 + 21 =

4. 3 – 15 =

5. 4 – 17 =

6. 4 – 21 =

7. –3 + 2 =

8. –5 + 2 =

9. –8 + 5 =

10. –5 + 6 =

11. –9 + 3 =

12. – 4 + 3 =

13. –2 – 5 =

14. –1 – 7 =

15. –5 – 5 =

16. 7 + 3 – 15 = ……… – ………

= ……………

17. 8 + 4 – 17 =

18. 2 + 4 – 21 =

19. –2 – 11 + 3 = ………..+……….

= ………

20. –3 – 15 + 8 = ……….. + ……….

= ……………….

21. 3 – 9 + 2 =

22. –3 – (–2) – 8

= ………. ………. – …….…

=…………. –………..

= ……………….

23. –1 – (–2) – 3

24. 4 – (–3) – 9

25. –3 + (–2) – 8

26. –3 + (–8) – 8 =

27. –4 + (–1) – 9

28. –3 – (–10) – (-2)

29. -5 – 17 – (–7)

30. -2 – 1 – (–17)


2

Multiplication of integers + × + = + + × − = − − × + = − − × − = +

1. –8 x 8 =

2. –2 x 12 =

3. – 3 x 8 =

4. –5 x (–5) =

5. –6 x (–6) =

6. –9 x (–9) =

7. 2 x (–3)

8. 9 x (–2) =

9. 23 x (–23) =

10. –7 x 6 x (–2 )

= …….…… x (–2 )

= ……………

11. –1 x 2 x (–3 )

= ………. x ………

= …………..

12. –5 x 4 x (–3)

13. 8 x (–2 ) x 9 =

= ……….. x ………..

=…………

14. 9 x (–10) x 2

15. 5 x (–5 ) x (–5)

16. –1 x (–2 ) x (–3 )

= ……….. x ………….

= ………………

17. –5 x (–6 ) x (–1)

18. –1 x (–3) x (–5)

Division of integers + ÷ + = + + ÷ − = − − ÷ + = − − ÷ − = +

1. 0 ÷ 1000 =

2. 121 ÷ 11 = 3. 35 ÷ 7

4. –25 ÷ 5 =

5. –42 ÷ 7 =

6. –56 ÷ 8 =

7. 64 ÷ (–8)

8. 72 ÷ (–8) =

9. 100 ÷ (–10) =

10. –121 ÷ (–11) =

11. –180 ÷ (–15) =

12. –234 ÷ (–18) =

13. 210 ÷ (–15) ÷ 1

= ……….. ÷ 1

= …………..

14. 120 ÷ (– 2) ÷ (–4)

15. -384 ÷ (–8) ÷ (–3)

16. −84

12=

17. −225

−15 = 18.

56

−2


3

Combined Operation of Addition, subtraction, Multiplication and Division of Integers

[Note: ………………………………………………………………………………………..]

5 + 8 − 13

=…………….. – 13

= …………….

6 − 10 + 13

−6 − 7 − 13

5 − (−6) + −7

=5 6 7

= ……… 7

= …………

−8 − (−5) − −7

10 − 15 + (−5)

8 + −2 × (−5)

= 8 ………..

= …………….

−8 + −7 × (−1)

−10 + −5 × (−3)

−3 × 8 + (−2)

= …………. …………

= ………….

−5 × −8 − (−18)

5 × −2 + (−10)

15 ÷ −3 + 5(−2)

= ………… ………….

= …………………

−15 ÷ −5 + 12 ÷ −3

−15 ÷ −5 + 12 ÷ −3

−5 × −5 − 12 ÷ −3

= …………. …………

= ……………….

30 ÷ −2 + 12 ÷ −3

−64 ÷ −8 − 12 × −3

2 [ 12 − 2 ÷ −5 + 2 −4 ]

−8 − 2 ÷ −2 × 2 −4 ÷ 2

8 × 2 + 5 − 4 − 2 × 8 — (−6)


4

Problem Solving

11 boxes containing 60 oranges each is divided equally among 22 students. How many oranges will each of them receive? Answer: 20

The average income of a hawker selling lime juice is RM 45 per day. What is his total income for six days?

Yee Sheng, Wen Jie and Mun Hong share a business. In the first 6 months, the business made a total loss of RM 900. If they share the loss equally, what is the loss for each of them in every single month? Answer: RM 50

The temperature in Mongolia dropped 16oC steadily from 6 p.m to 10 p.m. . Find the average drop in temperature per hour. Answer: -4oC

In a quiz competition, every contestant must answer 25 questions. Each correct answer is awarded 8 marks but 4 marks are deducted for every incorrect answer. Roslan answered 20 questions correctly while Jason answered 16 questions correctly. Find the difference in their marks.

William, Steven, Willy and Henry bought some shares in Jun. They suffered a loss of RM 5600 in July. If they divided the loss equally, find the amount that William and Steven lost. Answer: - RM 2800

A car needs 19 litres of petrol to travel a distance of

247 km. what I s the average distance it can travel

on a litre of petrol. Answer: 13 km

The temperature of a certain liquid in the refrigerator is

-3oC. 15 minutes later the temperature of the liquid

increase by 2oC. The liquid is then heated and its

temperature increases by 23oC. What is the temperature

of the liquid now?


5

Positive and Negative Fractions

Positive and Negative integers

Compare and order fractions

A fraction is always greater than the fraction to its left.

Fill in each box below with or

−𝟏

𝟒

𝟏

𝟑

𝟏

𝟓 −

𝟐

𝟑

−𝟏

𝟓 −

𝟐

𝟓

−𝟏

𝟒

𝟐

𝟑

−𝟏

𝟒 1

𝟏

𝟑 −𝟐

𝟑

𝟕 2

𝟏

𝟑 −𝟐𝟑

𝟏

𝟒 −1

𝟏

𝟐 −𝟐

𝟑

𝟕 2

𝟏

𝟑

𝟏

𝟐

𝟏

𝟑

………. …………

𝟑

𝟓

𝟑

𝟒

………. …………

𝟐

𝟑

𝟓

𝟔

………. …………

𝟓

𝟔

𝟓

𝟕

………. …………

−𝟏

𝟒 −

𝟐

𝟑

………. …………

−𝟏

𝟔 −

𝟐

𝟓

………. …………

−𝟓

𝟖 −

𝟐

𝟓

………. …………

−𝟑

𝟕 −

𝟐

𝟗

………. …………

−𝟏𝟏

𝟒 −1

𝟐

𝟑

………. …………

………. …………

−𝟐𝟏

𝟐 −2

𝟏

𝟒

………. …………

………. …………

𝟑𝟐

𝟑 3

𝟏

𝟔

………. …………

………. …………

𝟓𝟐

𝟕 5

𝟏

𝟑

………. …………

………. …………


6

Arrange the following fractions in ascending and descending order.

means increasing

means decreasing.

𝟏

𝟐 , −

𝟓

𝟔 ,

𝟐

𝟑 , −

𝟒

𝟓

……… , ……… , ……… , ……… Answer: Ascending order:

, , , Descending order:

, , ,

𝟏

𝟐 , −

𝟐

𝟓 ,

𝟐

𝟏𝟎

……… , ……… , ……… Answer: Ascending order:

, , Descending order:

, ,

𝟏

𝟐 , −

𝟐

𝟑 ,

𝟏

𝟒 −

𝟓

𝟏𝟐

……… , ……… , ……… , ……… Answer: Ascending order:


, , ,

𝟏

𝟐 , −𝟏

𝟏

𝟒 , 𝟏

𝟏

𝟓 − 𝟏

𝟑

𝟏𝟎

……… , ……… , ……… , ……… ……… , ……… , ……… , ……… Answer: Ascending order:


, , ,

−𝟐𝟏

𝟐 , −𝟏

𝟏

𝟖 , −𝟏

𝟏

𝟒 − 𝟐

𝟑

𝟏𝟔



, , ,

𝟐𝟏

𝟐 , 𝟏

𝟐

𝟑 , −𝟏

𝟏

𝟒 𝟐

𝟏

𝟔



, , ,

Addition and subtraction of fractions

−7

9− −

2

3 = −

7

9+

2

3

= −7

9+

6

9

= …………..

−7

18− −

2

3 =

Answer: 𝟓

𝟏𝟖

−7

3− −

2

9 =

Answer: −𝟐𝟏

𝟗

−7

5− −

2

2 =

−4

15− −

1

3 =

−2

3− −

5

9 =


7

−2

5+ −

2

3

= −2

5−

2

3

= −6

15−

10

15

= −16

15

= −11

15

−2

4+ −

2

5 =

Answer: −𝟗

𝟏𝟎

−2

3+ −

2

7 =

Answer: −𝟐𝟎

𝟐𝟏

−11

2+ −1

1

3 − −1

1

12 =

= −3

2−

4

3+

13

12

= −18

12−

16

12+

13

12

= −24

12+

13

12

= ……….

−1

2+ −2

1

3 − −2

1

6 =

Answer: −𝟐

𝟑

3

5+ −2

1

3 —

1

15=

Answer: −𝟏𝟒

𝟓

−45

6+ 3

3

8− −1

3

4 =

= −29

6+

27

8+

7

4

= −116

24+

81

24+

42

24

= −35

24+

42

24

= …………….

−41

4+ 2

3

8− −1

3

10 =

Answer: −𝟐𝟑

𝟒𝟎

−11

2+ 3

2

3− −1

3

4 =

Answer: 𝟑𝟏𝟏

𝟏𝟐

−67

9− −4

7

12 − 3

1

6=

= −61

9+

55

12−

19

6

= −244

36+

165

36−

114

36

= −79

36−

114

36

= −193

36

= …………..

−27

9− −3

7

12 − 2

1

6=

Answer: −113

36

−17

9− −

7

12 − 3

1

6=

Answer: −413

36


8

Multiplication of fractions

−3

4 × 2 =

−3

8 × (−40) =

5 × −2

15 =

−3

16 × (−8) =

−3

9 × (−45) =

25 × −2

15 =

3

4 × −

16

27 =

−3

4 × −

3

5 =

−11

4 × −1

2

3 =

−11

4 × −2

5

12 =

−11

4 × −

8

15 =

−1

4 × −

8

15 =

−1

4 × −

5

12 × 1

1

4 =

−21

3 × −

1

2 × (−1

1

2) = −2

1

3 × −

1

2 × (−1

1

2) =

4

15 × −

5

12 × 2

1

3 =

14

5 × −1

5

9 × 1

1

7 =

−12

3 × −4

5

6 × −7

8

9 =


9

Division of fractions

5

8÷

24

25=

−4

7÷ −

9

10 = −

5

12÷

3

20=

23

7÷ 5

2

3=

−12

5÷ 3

3

4= −1

5

7÷ −1

5

6 =

72

5÷ −3

3

11 ÷ −5

1

2 =

−81

4÷ −3

3

8 ÷ −2

4

5 =

69

11÷

25

44÷ −7

4

5 =

−21

2÷ −3

3

8 ÷ −1

1

9 =

−32

5÷ 4

1

4÷

10

13= −1

8

15÷ −5

5

8 ÷ −

16

25 =


10

Positive and Negative Decimals

Convert the following fraction into the decimals 1

2=

1×5

2×5

=5

10

= …………..

𝟑

𝟒 =

𝟐

𝟓 =

5

8=

7

16=

1

40=

Compare and order decimals

A decimal is always greater than the decimal to its left.

Fill in each box below with or

−0.25 0.3

0.2 −0.666

−0.2 −0.4

−0.25 0.88

−0.25 1.55 −2.8 2.9 −23.6 −1.5 −2.37 2.13

0.5 0.8 0.6 0.75

3.8 5.6

5.6 5.7

−0.25 −0.24

−0.13 −0.12

−5.8 −2.5

−7.7 −7.8

−1.25 0 −3.25 −5.25

3.8 3.6

5.89 5.99


11

Addition and Subtraction of decimals

0.5 − 2.1 =

3.2 − 2.5 = 3.8 − 9.9 =

−0.5 − 1.6 =

−3.2 + 6.5 = 1.8 − 0.9 =

0.6 + (- 1.3) =

−2.6 −(−1.8) = −1.2 + 5.2 =

−0.3 + (− 0.7) =

0.7 – (−0.2) = −0.8 − 1.24 =

3.24 + (−0.25) + (−4.62)

− 0.37 + (−6.24) + (−3.21) −8.245 – (−5.113) –(−0.456)

1.25 + (−0.15) + (−2.63)

− 1.37 + (−3.24) + (−2.21) −2.245 – (−5.213) –(−0.56)

− 0.32 − [1999 + (−2001)]

0.72 − (− 0.00405 – 2.1) 0.0001 – (−0.002) + (−1.23)

4.235 + −6.563 − ( −10.999)

−10.01 − 8.9 − (−9.99) −9.8 − 0.55 − (−32.2)


12

Multiplication of decimals

1.2 × 3 =

−0.2 × 6 =

−1.6 × (−2) =

0.3 × 0.2 = −0.1 × (−0.02) = 0.11 × 0.02 =

0.8 × −1.2 = −0.3 × −0.7 = 1.3 × −6.1 =

−3.7 × 1.5 = −0.004 × 0.9 = 0.2 × −1.4 =

−0.9 × 0.9 × 0.1 =

= −0.81 × 0.1

= ………………………….

0.36 × −2.4 × −0.2 =

−8.1 × −0.2 × 1.1

−0.9 × (−0.2) × 3 =

= ……………….. × 3

= ………………..

3.6 × −3.4 × −0.1 =

−8.1 × −0.01 × 0.1

−0.4 × 0.06 × (−1.2) =

0.36 × −2.4 × −0.2 =

−8.1 × −0.2 × 1.1

−0.2 × (−0.02) × 0.002 =

1.2 × −1.3 × 1.1 =

−2.1 × −0.2 × 0.02

−0.04 × 2.2 × (−3.3)

−3.2 × 0.5 × 1.2 =

0.5 × 2.4 × 0.001 =

−0.1 × 02 × (−0.3) =

0.6 × −2.1 × −0.3 =

−1.1 × −0.2 × (−0.1)


13

Division of decimals

2.5 ÷ 5 =

–4.2 ÷ 6 = −0.008 ÷ 2 =

2.5 ÷(– 0.5) =

= –25 ÷ (–5)

= …………..

–4.2 ÷ 0.6 =

–0.008 ÷ 0.2 =

3 ÷ 0.02 =

= 3 00 ÷ 2

= …………….

–0.888 ÷ (–0.88) = –0.008 ÷ 0.002 =

3.5 ÷ (–0.5) ÷ 0.01 =

= 350 ÷ (–5) ÷ 0.01

= -70 ÷ 0.01

= -7000 ÷ 1

= ………………

-2.3 ÷ (–0.02) ÷ (–0.001) = -4 ÷ (–0.02) ÷ (–0.2) =

2.5 ÷ (–0.01) ÷ 0.1

= –250 ÷ 1 ÷ 0.1

= –250 ÷ 0.1

= –2500 ÷ 1

= ……..…..

9.61 ÷ (–3.1) ÷ 0.01

-6.60 ÷ (–0.02) ÷ 0.11

0.55 ÷ (–0.11) ÷ 5 =

2.2 ÷ (–0.02) ÷ 11 =

-1.44 ÷ (–1.2)÷ (-0.2) =

0.5

0.01=

50

1

= …………..

0.02

−0.2=

−0.121

−0.11=

−6.5

0.13=

6.4

0.01=

1.5

−0.3=

−6.5

0.13=

−2.71

−0.23=

−28.9

−1.4=


14

Computation involving the combination of two or more operations on directed number

[55 + −37 ] × 6

[32 − −38 ] × 0.5

2[32 − −38 ] ÷ 0.5

1

4− −6.02 ÷ 5

1

4+ −0.5 ÷ 0.5

2 1

4− 2.5 ÷ 0.2

−2.2 − 0.6 +1

7÷

1

14

= −2.2 − ( 0.6 + 1

7 ×

14

1)

= −2.2 − ( 0.6 + ………..)

= −2.2 − …………..

= ………………

−7.32 − 0.36 +1

7÷

5

14

−5.2 + 0.3 +1

3÷

5

18

[21

7+ −

6

7 ] ÷ −

5

3 ×

5

9

= 15

7−

6

7 ÷ −

5

3 ×

5

9

=9

7× −

3

5 ×

5

9

= ……………

[21

3+ −

1

6 ] ÷ −

5

6 ×

5

9

−42

5+ −2

1

3− −1

1

9 ÷ 1

5

6

−4.6 − 2.3 × 0.2 + −3.7

−2.6 ÷ 0.2 × 0.2 + −1.6

−2

5÷ 0.4 − 35 ÷ 0.7

−0.63 + 9.27 ÷ 14

5

6.3 ÷ 0.9 − −4.1 × 0.4 2.26 − (1.4 + 1

6÷

5

18)


15

Posing and solving problems involving directed numbers

From the surface of the sea, a submarine descends 2.5 m per minute. After descending steadily for 20 minutes, it then ascends 12.7 m and descends another 27.56 m. Find its final distance from the surface. Answer: 64.86 below the sea level.

A submarine is 3051

2 𝑚 below the surface of the sea. It

rises 2501

2 𝑚 and then submerges725

1

4 𝑚. Find its

new position from the surface of the sea. Answer: 𝟕𝟖𝟎

𝟏

𝟒 m

In a quiz, each participant is required to answer 40 questions. 2 marks are given for each correct answer, 0.5 marks is deducted for each wrong answer and 1 mark is deducted for each unanswered question. Ravi answers 30 questions correctly and 4 questions wrongly. Calculate the total marks obtained by Ravi. Answer: 52

An old folks’ home has 32 occupants. During a

celebration, a biscuit company presented 21

4kg of

biscuits to each occupant Find the total mass of biscuits the company had to prepare. Answer: 72 kg

In a computer quiz, contestants were given 3 points for a correct answer but -2 points for an incorrect answer. Weng Hong answered 12 question correctly and 5 questions incorrectly. What was his score? Answer: 26 points

If eight pencils cost at total of RM 0.48, how many pencils can be purchased with RM 1.02. Answer: 17 pencils


16

ENRICHMENT EXERCISE: 3

10+

4

1000+

5

𝑓= 0.354, find the value of f.

Answer: 100

5+8−1

23

−3

1+ −1

3 × −2

10

11

ANSWER: 1𝟕

𝟏𝟓

−8.7 + 6 − 5

12× −28.8

ANSWER: 9.3

14.4 × −2.75 − −2

3 ÷ 5

ANSWER: 6

Find the value of 7.7

0.77+

7.7

0.77÷

0.073

7.3

Answer : 1010

Find the value of 105 ÷ 5 + 15 x 3 – (6 x 12 – 54 ÷ 9 ) Answer: 0


17

Hot air balloon X and Y are at the same height. Balloon X rises 360 m and goes down 2/3 of the distance. At the same time balloon Y goes down 243.5 m. Find the distance in height between the two balloons. Answer: 363.5 m

Matthew spent 25% of the money he had on magazines and 60% of the remaining money on a novel. If he then had RM 7.50 left, how much did he spend on the novel? Answer: RM 11.25

A long-distance telephone call cost RM 1.60 for the first 5 minutes and RM 0.30 for each additional minute. He Lin made a long-distance telephone call and was charged RM 4.30. How long did He Lin’s telephone call last? Answer: 14 minutes

Pin Shen’ motorcycle can hold 10 litres of petrol in its fuel tank. It can travel 40 km on one litre of petrol. On Friday, he fills up the tank and travel 90 km. on

Saturday, he travels 25

18 of Friday’s distance. On

Sunday, he travels 0.5 of Friday’s distance. He then fills his tank with 3 litres of petrol. How much petrol is there in his tank now?

In a quiz competition of 20 questions, 4 marks are given for a correct answer and 2 marks are deducted for a wrong answer James answered 11 questions correctly and Susan answered 15 questions incorrectly. What is the difference between their marks? Answer: 36

Below are five number cards

Find the sum of two cards with the largest and smallest number. Answer: 9 or -3 / 6


18

Chapter 1 Directed Number (2)

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Transcript of Chapter 1 Directed Number (2)